Research Article
Simulation of a Jackson tandem network using state-dependent importance sampling
@INPROCEEDINGS{10.4108/ICST.VALUETOOLS2008.4370, author={D.I. Miretskiy and W.R.W. Scheinhard and M.R.H. Mandjes}, title={Simulation of a Jackson tandem network using state-dependent importance sampling}, proceedings={3rd International ICST Conference on Performance Evaluation Methodologies and Tools}, publisher={ICST}, proceedings_a={VALUETOOLS}, year={2010}, month={5}, keywords={Rare event simulation importance sampling state-dependent change of measure asymptotic optimality tandem queue}, doi={10.4108/ICST.VALUETOOLS2008.4370} }- D.I. Miretskiy
W.R.W. Scheinhard
M.R.H. Mandjes
Year: 2010
Simulation of a Jackson tandem network using state-dependent importance sampling
VALUETOOLS
ICST
DOI: 10.4108/ICST.VALUETOOLS2008.4370
Abstract
This paper considers importance sampling as a tool for rare-event simulation. The focus is on estimating the probability of overflow in the downstream queue of a Jackson two-node tandem queue. It is known that in this setting 'traditional' state-independent importance-sampling distributions perform poorly. We therefore concentrate on developing a state-dependent change of measure that is provably asymptotically efficient.
More specific contributions are the following. (i) We concentrate on the probability of the second queue exceeding a certain predefined threshold before the system empties. Importantly, we identify an asymptotically efficient importance-sampling distribution for any initial state of the system. (ii) The choice of the importance-sampling distribution is backed up by appealing heuristics that are rooted in large-deviations theory. (iii) Our method for proving asymptotic efficiency is substantially more straightforward than some that have been used earlier.